A 120\/208 V distribution transformer bank of three single phase transformers is connected as a four wire {D pri. – YN sec.} with Neutral wire at the secondary side to service different load demand of 120\/208 Vac. The transformer turn ratio is 100:1. The load in the system consists of ONE 72KW , 3 phase motor with PF =1 operating at Vt of 208V; THREE 12KW, 1 phase lighting circuits with a terminal voltage of 120V; and THREE 1 phase 10 KVA motors, PF=0.8 lagging with the terminal voltage of 208 V. Calculate<\/p>\n\n\n\n
*The KVA rating of the individual transformers (KVA\/Transformer bank) to be used knowing that 50KVA, 100KVA and 150KVA is available in the market<\/p>\n\n\n\n
*The full line currents (in AMPS) on the high voltage side of the transformer using a transformer rating of 150KVA<\/p>\n\n\n\n
*The Vline at the primary side of transformer in KV<\/p>\n\n\n\n
*The KVA of the transformer bank if ratings of 100KVA, 112.5 KVA and 150KVA & 200KVA are only available in the market!<\/p>\n\n\n\n
*The primary line current in AMPS<\/p>\n\n\n\n
*The Vline in KV at the secondary side of transformer<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n Total kVA load:<\/strong> The system uses a \u0394-Y<\/strong> connection, so the total kVA is divided equally among the three transformers.<\/p>\n\n\n\n [ The closest available transformer rating is 50 kVA<\/strong>, so we select three 50 kVA transformers<\/strong>.<\/p>\n\n\n\n The HV side is delta-connected with a primary voltage of 12 kV (assuming 12 kV primary for 120\/208 V secondary)<\/strong>.<\/p>\n\n\n\n Total bank rating: 150 kVA<\/strong> (since we chose 50 kVA per transformer). [ [ The secondary side voltage is 208 V (line-to-line)<\/strong>.<\/p>\n\n\n\n [ [ Given the transformer ratio 100:1<\/strong>, the primary line voltage:<\/p>\n\n\n\n [ Available options: 100 kVA, 112.5 kVA, 150 kVA, 200 kVA<\/strong> [ [ The secondary voltage remains:<\/p>\n\n\n\n [ This ensures that the transformer bank is adequately rated for safe and efficient operation.<\/p>\n","protected":false},"excerpt":{"rendered":" A 120\/208 V distribution transformer bank of three single phase transformers is connected as a four wire {D pri. – YN sec.} with Neutral wire at the secondary side to service different load demand of 120\/208 Vac. The transformer turn ratio is 100:1. The load in the system consists of ONE 72KW , 3 phase […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-204761","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/204761","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=204761"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/204761\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=204761"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=204761"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=204761"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Solution: Distribution Transformer Bank Calculations<\/strong><\/h3>\n\n\n\n
Step 1: Calculate the Total Load in kVA<\/strong><\/h4>\n\n\n\n
\n
[
S_{3\\phi} = \\frac{P}{PF} = \\frac{72}{1} = 72 \\text{ kVA}
]<\/li>\n\n\n\n
[
S_{\\text{lights}} = 3 \\times 12 = 36 \\text{ kVA}
]<\/li>\n\n\n\n
[
S_{\\text{1\u03d5 motors}} = 3 \\times 10 = 30 \\text{ kVA}
]<\/li>\n<\/ol>\n\n\n\n
[
S_{\\text{total}} = 72 + 36 + 30 = 138 \\text{ kVA}
]<\/p>\n\n\n\n
\n\n\n\nStep 2: Determine kVA per Transformer<\/strong><\/h4>\n\n\n\n
S_{\\text{per transformer}} = \\frac{S_{\\text{total}}}{3} = \\frac{138}{3} = 46 \\text{ kVA}
]<\/p>\n\n\n\n
\n\n\n\nStep 3: Full Line Current on the High Voltage (HV) Side<\/strong><\/h4>\n\n\n\n
HV line voltage: 12 kV<\/strong>
Delta connection formula for HV line current:<\/p>\n\n\n\n
I_{\\text{HV}} = \\frac{S_{\\text{total}}}{\\sqrt{3} V_{\\text{line HV}}}
]<\/p>\n\n\n\n
I_{\\text{HV}} = \\frac{150}{\\sqrt{3} \\times 12} = \\frac{150}{20.78} = 7.22 \\text{ A}
]<\/p>\n\n\n\n
\n\n\n\nStep 4: Secondary Line Current<\/strong><\/h4>\n\n\n\n
I_{\\text{secondary}} = \\frac{S_{\\text{total}}}{\\sqrt{3} V_{\\text{line secondary}}}
]<\/p>\n\n\n\n
I_{\\text{secondary}} = \\frac{138}{\\sqrt{3} \\times 208} = \\frac{138}{360.13} = 383.3 \\text{ A}
]<\/p>\n\n\n\n
\n\n\n\nStep 5: Primary Line Voltage<\/strong><\/h4>\n\n\n\n
V_{\\text{line primary}} = \\frac{208}{100} = 12 \\text{ kV}
]<\/p>\n\n\n\n
\n\n\n\nStep 6: Choosing kVA of Transformer Bank<\/strong><\/h4>\n\n\n\n
Since we need at least 138 kVA<\/strong>, we select 150 kVA<\/strong> (3 \u00d7 50 kVA).<\/p>\n\n\n\n
\n\n\n\nStep 7: Primary Line Current<\/strong><\/h4>\n\n\n\n
I_{\\text{primary}} = \\frac{S_{\\text{bank}}}{\\sqrt{3} V_{\\text{primary}}}
]<\/p>\n\n\n\n
I_{\\text{primary}} = \\frac{150}{\\sqrt{3} \\times 12} = 7.22 \\text{ A}
]<\/p>\n\n\n\n
\n\n\n\nStep 8: Secondary Line Voltage<\/strong><\/h4>\n\n\n\n
V_{\\text{line secondary}} = 208V = 0.208 \\text{ kV}
]<\/p>\n\n\n\n
\n\n\n\nFinal Answers:<\/strong><\/h3>\n\n\n\n
\n